Sparse representation of two- and three-dimensional images with fractional Fourier, Hartley, linear canonical, and Haar wavelet transforms

Sparse recovery aims to reconstruct signals that are sparse in a linear transform domain from a heavily underdetermined set of measurements. The success of sparse recovery relies critically on the knowledge of transform domains that give compressible representations of the signal of interest. Here we consider two- and three-dimensional images, and investigate various multi-dimensional transforms in terms of the compressibility of the resultant coefficients. Specifically, we compare the fractional Fourier (FRT) and linear canonical transforms (LCT), which are generalized versions of the Fourier transform (FT), as well as Hartley and simplified fractional Hartley transforms, which differ from corresponding Fourier transforms in that they produce real outputs for real inputs. We also examine a cascade approach to improve transform-domain sparsity, where the Haar wavelet transform is applied following an initial Hartley transform. To compare the various methods, images are recovered from a subset of coefficients in the respective transform domains. The number of coefficients that are retained in the subset are varied systematically to examine the level of signal sparsity in each transform domain. Recovery performance is assessed via the structural similarity index (SSIM) and mean squared error (MSE) in reference to original images. Our analyses show that FRT and LCT transform yield the most sparse representations among the tested transforms as dictated by the improved quality of the recovered images. Furthermore, the cascade approach improves transform-domain sparsity among techniques applied on small image patches. © 2017 Elsevier Lt

Speech signal compression and encryption based on sudoku, fuzzy C-means and threefish cipher

Compression and encryption of speech signals are essential multimedia technologies. In the field of speech, these technologies are needed to meet the security and confidentiality of information requirements for transferring huge speech signals via a network, and for decreasing storage space for rapid retrieval. In this paper, we propose an algorithm that includes hybrid transformation in order to analyses the speech signal frequencies. The speech signal is then compressed, after removing low and less intense frequencies, to produce a well compressed speech signal and ensure the quality of the speech. The resulting compressed speech is then used as an input in a scrambling algorithm that was proposed on two levels. One of these is an external scramble that works on mixing up the segments of speech that were divided using Fuzzy C-Means and changing their locations. The internal scramble scatters the values of each block internally based on the pattern of a Sudoku puzzle and quadratic map so that the resulting speech is an input to a proposed encryption algorithm using the threefish algorithm. The proposed algorithm proved to be highly efficient in the compression and encryption of the speech signal based on approved statistical measures

Comparative analysis of different approaches to target differentiation and localization with sonar

Cataloged from PDF version of article.This study compares the performances of di erent methods for the di erentiation and localization of commonly encountered features in indoor environments. Di erentiation of such features is of interest for intelligent systems in a variety of applications such as system control based on acoustic signal detection and identi/cation, map building, navigation, obstacle avoidance, and target tracking. Di erent representations of amplitude and time-of-2ight measurement patterns experimentally acquired from a real sonar system are processed. The approaches compared in this study include the target di erentiation algorithm, Dempster–Shafer evidential reasoning, di erent kinds of voting schemes, statistical pattern recognition techniques (k-nearest neighbor classi/er, kernel estimator, parameterized density estimator, linear discriminant analysis, and fuzzy c-means clustering algorithm), and arti/cial neural networks. The neural networks are trained with di erent input signal representations obtained using pre-processing techniques such as discrete ordinary and fractional Fourier, Hartley and wavelet transforms, and Kohonen’s self-organizing feature map. The use of neural networks trained with the back-propagation algorithm, usually with fractional Fourier transform or wavelet pre-processing results in near perfect di erentiation, around 85% correct range estimation and around 95% correct azimuth estimation, which would be satisfactory in a wide range of applications. (C) 2002 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserve

Characterization and design of coherent optical OFDM transmission systems based on Hartley Transform

Nowadays, due to huge deployment of optical transport networks, a continuous increase towards higher data rates up to 100 Gb/s and beyond is observed. Furthermore, an evolution of the current optical networks is forecasted, acquiring new functionalities, e.g. elastic spectrum assignment for the optical signals. The target for these new challenges in transmission is to find techniques ready to deal with a growth of demand for bandwidth continuously asked by network operators, for whom the standard systems do not meet the new functionalities while higher rates are being set up. A solution for covering all of those needs is to adapt techniques capable to deal with such enormous data rates, and ensuring the same high efficiency for long distances and mitigate the optical impairments accumulated along the transmission path. Additionally, these transmission techniques are expected to provide some degree of flexibility, in order to enhance the network flexibility. A promising technology that can fully cope with those requires is the coherent optical orthogonal frequency division multiplexing (CO-OFDM). CO-OFDM provides several advantages, namely high sensitivity and spectral efficiency, simple integration and possibility to fully recover a signal in phase, amplitude and polarization. These systems are composed by digital signal processing (DSP) blocks that easily process data and can equalize and compensate the main impairments, providing high tolerance for dispersion effects. However, CO-OFDM systems are not free from drawbacks. Their high peak-to-average power ratio (PAPR) reduce their tolerance to nonlinearities. Furthermore, CO-OFDM systems are sensitive to any frequency shift and phase offset. Hence, a constant envelope optical OFDM (CE-OFDM) is proposed for significantly reducing the PAPR and solving high sensitivity to nonlinear impairments. It consists in a phase modulated discrete multi-tone signal, which is coherently detected at the receiver side. An alternative transform, the discrete Hartley transform, is proposed to speed up calculations in the DSP and eliminate the need to have a Hermitian symmetry. The optical CE-OFDM by its unique flexibility and rate scalability turns out as a great technology applicable to different configurations, ranging from access to core networks. In case of access solutions, several cases are investigated. First, the optical CE-OFDM is applied for radio access network signals delivery by means of a wavelength division multiplexing (WDM) overlay in deployed access architecture. A decomposed radio access network is deployed over an existing standard passive optical network (PON), capable to avoid interference and cross talks with access signals between network clients. The system exhibited narrow channel spacing, while reducing losses fed into the access equipment path. Next, a full duplex 10 Gb/s bidirectional PON transmission over a single wavelength with RSOA based ONU is investigated. The key point of that system is the upstream transmission, which is achieved re-modulating the phase of a downstream intensity modulated signal after proper saturation. The reported sensitivity performances show a power budget matching the PON standards and an OSNR easy to reach on non-amplified PON. Next, a flexible metropolitan area network of up to 100km with traffic add/drop using WDM is investigated. There the narrowing effect of the optical filters is studied. Finally, an elastic upgrade of the existing Telefonica model of the Spanish national core network is proposed. For that, the transceiver architecture is proposed to be operated featuring polarization multiplexing. Respect to the existing fixed grid, the flexible approach (enabled by the CE-OFDM transceiver) results into reduced bandwidth occupancy and low OSNR requirement.Hoy en día, debido al gran despliegue de las redes de ópticas de transporte, se espera un aumento continuado hacia mayores velocidades de datos, hasta 100 Gb/s y más allá. Por otra parte, la evolución que se prevé para las redes ópticas actuales, incluye la adquisición de nuevas funcionalidades, por ejemplo, la asignación del espectro de forma elástica para las señales ópticas. Por tanto, el claro desafío en cuanto a las tecnologías de transmisión es encontrar técnicas preparadas para hacer frente a un crecimiento de la demanda de ancho de banda; demanda que continuamente se incrementa por parte de los operadores de red, para quienes los sistemas estándar no se acaban de ajustar a las nuevas funcionalidades que esperan para la red. Una solución para cubrir todas estas necesidades es la adaptación de técnicas capaces de hacer frente a estas velocidades de datos enormes, y garantizar el mismo nivel de eficiencia para las largas distancias y mitigar las deficiencias ópticas acumuladas a lo largo de la ruta de transmisión. Además, se espera que estas técnicas de transmisión puedan proporcionar cierto grado de flexibilidad, a fin de mejorar y hacer más eficiente la gestión de la red. Una tecnología prometedora que puede hacer frente a estos requisitos es lo que se llama multiplexación por división de frecuencias ortogonales, combinado con la detección óptica coherente (CO-OFDM). CO-OFDM ofrece varias ventajas, entre otras: alta sensibilidad y eficiencia espectral y, sobre todo, la posibilidad de recuperar por completo de una señal en fase, la amplitud y la polarización. Estos sistemas están compuestos por bloques de procesado de señales digitales (DSP) que permiten detectar los datos fácilmente así como también compensar las principales degradaciones, proporcionando alta tolerancia a los efectos de dispersión. Sin embargo, los sistemas CO-OFDM no están exentos de inconvenientes. Su alta relación de potencia de pico a potencia media (PAPR) reduce sensiblemente la tolerancia no linealidades. Por otra parte, los sistemas CO-OFDM son sensibles a cualquier cambio de frecuencia y desplazamiento de fase. Por tanto, se propone un sistema OFDM de envolvente constante (CE-OFDM) para reducir significativamente la PAPR y solucionar la alta sensibilidad a las degradaciones no lineales. Consiste en una señal OFDM modulada en fase, que se detecta coherentemente en el receptor. Una transformada alternativa, la transformada discreta de Hartley, se propone para acelerar los cálculos en el DSP. El sistema CE-OFDM por su flexibilidad y escalabilidad única, resulta una tecnología aplicable a diferentes escenarios, que van desde las redes de acceso hasta las redes troncales. En el caso de las soluciones de acceso, se investigan varios casos. En primer lugar, el CE-OFDM aplica para el desarrollo y soporte de datos de una red radio, reutilizando una red óptica de acceso ya desplegada. A continuación, se investiga la transmisión bidireccional dúplex a 10 Gb / s sobre una sola longitud de onda empleando un RSOA a las unidades de usuario. El punto clave de este sistema es la transmisión en sentido ascendente, que se consigue re-modulando la fase de una señal de intensidad modulada después de saturar de forma adecuada. A continuación, se estudia una red de área metropolitana flexible de hasta 100 km. Concretamente el efecto de concatenación de filtros ópticos es el objetivo de este estudio. Finalmente, se propone una actualización elástica del modelo de Telefónica I+D para la red troncal española. Por ello, se propone operar el CE-OFDM en multiplexación de polarización. Los resultados muestran que esta combinación reduce sensiblemente el empleo de ancho de banda esto como los requisitos de los enlaces transmisión, reduciendo también los costes tanto de desarrollo como de operación y mantenimiento de la red.Avui dia, a causa del gran desplegament de les xarxes de òptiques de transport, s'espera un augment continuat cap a majors velocitats de dades, fins a 100 Gb/s i més enllà. D'altra banda, l'evolució que es preveu per a les xarxes òptiques actuals, inclou l'adquisició de noves funcionalitats, per exemple, assignació de l'espectre de forma elàstica per als senyals òptics. Per tant, el clar desafiament pel que fa a les tecnologies de transmissió és trobar tècniques preparades per fer front a un creixement de la demanda d'ample de banda; demanda que contínuament es fa per part dels operadors de xarxa, per als qui els sistemes estàndard no s'acaben d'ajustar a les noves funcionalitats que esperen per a la xarxa. Una solució per a cobrir totes aquestes necessitats és l'adaptació de tècniques capaces de fer front a aquestes velocitats de dades enormes, i garantir el mateix nivell d'eficiència per a les llargues distàncies i mitigar les deficiències òptiques acumulades al llarg de la ruta de transmissió. A més, s'espera que aquestes tècniques de transmissió puguin proporcionar cert grau de flexibilitat, per tal de millorar i tornar més eficient la gestió de la xarxa. Una tecnologia prometedora que pot fer front a aquests requisits és el que s'anomena multiplexació per divisió de freqüències ortogonals, combinat amb la detecció òptica coherent (CO-OFDM). CO-OFDM ofereix diversos avantatges, entre altres: alta sensibilitat i eficiència espectral i, sobretot, la possibilitat de recuperar per complet d'una senyal en fase, l'amplitud i la polarització. Aquests sistemes estan compostos per blocs de processament de senyals digitals (DSP) que permeten detectar les dades fàcilment així com també compensar les principals degradacions, proporcionant alta tolerància pels efectes de dispersió. No obstant això, els sistemes CO-OFDM no estan exempts d'inconvenients. La seva alta relació de potència de pic a potència mitjana (PAPR) redueix sensiblement la tolerància a no linealitats. D'altra banda, els sistemes de CO-OFDM són sensibles a qualsevol canvi de freqüència i desplaçament de fase. Per tant, es proposa un sistema OFDM d'envolvent constant (CE-OFDM) per a reduir significativament la PAPR i solucionar l'alta sensibilitat a les degradacions no lineals. Consisteix en un senyal OFDM modulat en fase, que es detecta coherentment en el receptor. Una transformada alternativa, la transformada discreta d'Hartley, es proposa accelerar els càlculs en el DSP. El sistema CE-OFDM per la seva flexibilitat i escalabilitat única, resulta una tecnologia aplicable a diferents escenaris, que van des de les xarxes d'accés fins a les xarxes troncals. En el cas de les solucions d'accés, s'investiguen diversos casos. En primer lloc, el CE-OFDM s'aplica per al desplegament i suport de dades d'una xarxa radio, reutilitzant una xarxa òptica d'accés ja desplegada. A continuació, s'investiga la transmissió bidireccional dúplex a 10 Gb/s sobre una sola longitud d'ona emprant un RSOA a les unitats d'usuari. El punt clau d'aquest sistema és la transmissió en sentit ascendent, que s'aconsegueix re-modulant la fase d'un senyal d'intensitat modulada després de saturar-la de forma adequada. A continuació, s'estudia una xarxa d'àrea metropolitana flexible de fins a 100 km. Concretament l'efecte de concatenació de filtres òptics és l'objectiu d'aquest estudi. Finalment, es proposa una actualització elàstica del model de Telefónica I+D per a la xarxa troncal espanyola. Per això, es proposa operar el CE-OFDM en multiplexació de polarització. Els resultats mostren que aquesta combinació redueix sensiblement l'ocupació d'ample de banda això com també els requisits dels enllaços transmissió, reduint també els costos tant de desplegament com d'operació i manteniment de la xarxa

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Transform pre-processing for neural networks for object recognition and localization with sonar

We investigate the pre-processing of sonar signals prior to using neural networks for robust differentiation of commonly encountered features in indoor environments. Amplitude and time-of-flight measurement patterns acquired from a real sonar system are pre-processed using various techniques including wavelet transforms, Fourier and fractional Fourier transforms, and Kohonen's self-organizing feature map. Modular and non-modular neural network structures trained with the back-propagation and generating-shrinking algorithms are used to incorporate learning in the identification of parameter relations for target primitives. Networks trained with the generating-shrinking algorithm demonstrate better generalization and interpolation capability and faster convergence rate. The use of neural networks trained with the back-propagation algorithm, usually with fractional Fourier transform or wavelet pre-processing results in near perfect differentiation, around 85% correct range estimation and around 95% correct azimuth estimation, which would be satisfactory in a wide range of applications. Neural networks can differentiate more targets, employing only a single sensor node, with a higher correct differentiation percentage than achieved with previously reported methods employing multiple sensor nodes. The success of the neural network approach shows that the sonar signals do contain sufficient information to differentiate a considerable number of target types, but the previously reported methods are unable to resolve this identifying information. This work can find application in areas where recognition of patterns hidden in sonar signals is required. Some examples are system control based on acoustic signal detection and identification, map building, navigation, obstacle avoidance, and target-tracking applications for mobile robots and other intelligent systems